This is an introductory course in number theory. The fundamental theorem of arithmetic is proved from the well-ordering principle, focusing on relative primeness and greatest common divisors. The infinity of prime numbers is established, and a study of their distribution is initiated. Congruence is introduced, yielding results like Fermat’s little theorem and Wilson’s theorem, and some of this is generalized using arithmetic functions. Then primitive roots are studied, culminating in quadratic reciprocity. Towards the end certain classes of numbers are treated, as well as other topics typical of number theory, like Diophantine equations, sums of squares and Fibonacci numbers.